To find the equations that reveal the solution of the equation [tex]x^2-25x+125=11[/tex], we are going to set the equation equal to 0 and solve for [tex]x[/tex]:
Step 1. Subtract 11 to both sides of the equation
[tex]x^2-25x+125-11=11-11[/tex]
[tex]x^2-25x-114=0[/tex]
Step 2. Factor the left hand side of the equation
[tex]x^2-25x-114=0[/tex]
[tex](x-6)(x-19)=0[/tex]
Step 3. Set each factor equal to zero and solve for [tex]x[/tex]
[tex]x-6=0[/tex] and [tex]x-19=0[/tex]
[tex]x=6[/tex] and [tex]x=19[/tex]
We can conclude that the equations that reveal the solution of the equation [tex]x^2-25x+125=11[/tex] are [tex]x=6[/tex] and [tex]x=19[/tex]
